The country of La la land has an agrarian economy and only produces food on a...

The country of La la land has an agrarian economy and only produces food on a fixed supply of land. The production of food per person hasn’t increased for a very long time even though better fertilizers have become available. Seeing this an economist tries to understand the country’s predicament using a mathematical model. Production in the model is given by a function that combines land and labor in the following way. Y = AL0.3N 0.7 Everything that is produced in the economy is consumed. I.e. C = Y . The economist also finds that the growth ratio of population given by N0 N has the following relationship with nutrition levels, measured by consumption per capita. N0 N = 0.5 C N 0.5 Note that N0 can be written as Nt+1 and N as Nt for notational purpose. (Show Work)

(a) Using equations in the question, write N0 in terms of the parameters A, L and population N.

(b) On a graph with N on the x-axis and N0 on the y-axis, show the country’s level of population in the long-run. Argue using the graph why this is the level of population.

(c) Compute the level of consumption per capita in the long-run.

Expert Solution

Rahul Sunny answered 2 years ago

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